The transient equations of viscous quantum hydrodynamics

We study the viscous model of quantum hydrodynamics in a bounded domain of space di-mension 1, 2, or 3; and in the full one-dimensional space. This model is a mixed order partial dierential system with nonlocal and nonlinear terms for the particle density, current density and electric potential. By a viscous regularization approach, we show existence and uniqueness of local in time solutions. We propose a reformulation as an equation of Schrodinger type, and we prove the inviscid limit